[SOLVED] Derivatives of real valued functions

Let f and g be twice differentiable real-valued functions defined on . If f'(x)>g'(x) , which of the following must be true for all x>0?
(a) f(x)>g(x)
(b) f''(x)>g''(x)
(c) f(x)-f(0)>g(x)-g(0)
(d) f'(x)-f'(0)>g'(x)-g'(0)
(e) f''(x)-f''(0)>g''(x)-g''(0)

The answer is c but I thought it was d. Can someone show me how to prove it is c?

Let f and g be twice differentiable real-valued functions defined on . If f'(x)>g'(x) , which of the following must be true for all x>0?
(c) f(x)-f(0)>g(x)-g(0)
Can someone show me how to prove it is c?

We know the derivative of is .
Therefore is increasing or .
Thus answer (c).